Introduction to hashing

On this and the following pages, we explore hashing, a technique
used (among other applications) to implement Java's common map
and set classes. Hashing is designed to solve the
problem of needing to efficiently find or store an item in a collection.
For example, if we have a list of 10,000 words of English and we want to check if a given
word is in the list, it would be inefficient to successively compare the word with
all 10,000 items until we find a match. Hashing is a technique to make things more
efficient by effectively narrowing down the search at the outset.

What is hashing?

Hashing means using some function or algorithm to map object data
to some representative integer value. This so-called hash code
(or simply hash) can then be used as a way to narrow down our search
when looking for the item in the map.

How hashing works

Purely as an example to help us grasp the concept, let's suppose that we want to
map a list of string keys to string values (for example, map a list of countries
to their capital cities). So let's say we want to store the data in Table 1 in
the map.

Key

Value

Cuba

Havana

England

London

France

Paris

Spain

Madrid

Switzerland

Berne

Table 1: Example data to put in a map

And let's suppose that our
hash function is to simply take the length of the string.
For simplicity, we'll have two arrays: one for our keys and one for the values. So to
put an item in the hash table, we compute its hash code (in this case, simply count
the number of characters), then put the key and value in the arrays at the corresponding
index. For example, Cuba has a hash code (length) of 4. So we store Cuba
in the 4th position in the keys array, and Havana in the 4th index of the
values array etc. And we end up with the following:

Position(hash code = key length)

Keys array

Values array

1

2

3

4

Cuba

Havana

5

Spain

Madrid

6

France

Paris

7

England

London

8

9

10

11

Switzerland

Berne

Now, in this specific example things work quite well. Our array needs to be big enough
to accommodate the longest string, but in this case that's only 11 slots. And we do waste
a bit of space because, for example, there's no 1-letter keys in our data, nor keys
between 8 and 10 letters. But in this case, the waste isn't so bad either.
And taking the length of a string is nice and fast, so so is
the process of finding the value associated with a given key
(certainly faster than doing up to five string comparisons)1.

We can also easily see that this method wouldn't work for storing arbitrary
strings. If one of our string keys was a thousand characters in length but the rest
were small, we'd waste the majority of the space in the arrays.
More seriously, this model can't deal with collisions: that is,
what to do when there is more than one key with the same hash code (in this case,
one than more string of a given length).
For example, if our keys were random words of English, taking
the string length would be fairly useless. Granted, the word psuedoantidisestablishmentarianistically would probably get its own place in the array.
But on the other hand, we'd be left with thousands of, say, 6-letter words all competing
for the same slot in the array.

Notes:
1. Incidentally, in this case, you may be wondering why we'd bother storing the
keys. But in the general case, we would need to check that the key in the map at
a given position is actually the one being sought.